Breakdown of nuclear quasi-equilibrium in highly compact binaries and the origin of the 2--3 hour gap in the orbital period distribution of cataclysmic variables

We have calculated the secular evolution of a highly compact binary, composed of a degenerate-dwarf primary and a low-mass main-sequence secondary, taking into account the combined effects of (1) the gradual breakdown of quasi-equilibrium of the 3He abundance in the interior of the secondary, and (2) the progressive mixture of fresh 3He into the core of the secondary due to the increasing depth of the stellar surface convection zone. We find that these effects may provide a natural explanation for the apparent sharp decrease in the discovery probability of a cataclysmic variable as its orbital period decreases through approx.3 hours. However, the effects that we consider do not account for the relatively large number of observed cataclysmic variables with orbital periods between approx.80 minutes and approx.2 hours, so that the overall distribution of orbital periods among cataclysmic variables is not yet fully understood